%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM017+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:13:09 PM UTC 2026
% Result : Theorem 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 212 ( 91 ~; 90 |; 26 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 51 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aElement0(X1)
& sdtmndtasgtdt0(xu,xR,X1)
& sdtmndtasgtdt0(xv,xR,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mWCRDef,axiom,
! [X1] :
( aRewritingSystem0(X1)
=> ( isLocallyConfluent0(X1)
<=> ! [X2,X3,X4] :
( ( aElement0(X2)
& aElement0(X3)
& aElement0(X4)
& aReductOfIn0(X3,X2,X1)
& aReductOfIn0(X4,X2,X1) )
=> ? [X5] :
( aElement0(X5)
& sdtmndtasgtdt0(X3,X1,X5)
& sdtmndtasgtdt0(X4,X1,X5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mWCRDef) ).
fof(mReduct,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aRewritingSystem0(X2) )
=> ! [X3] :
( aReductOfIn0(X3,X1,X2)
=> aElement0(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).
fof(m__656_01,hypothesis,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(m__779,hypothesis,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& sdtmndtasgtdt0(xv,xR,xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__779) ).
fof(m__755,hypothesis,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).
fof(m__731,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(c_0_8,negated_conjecture,
~ ? [X1] :
( aElement0(X1)
& sdtmndtasgtdt0(xu,xR,X1)
& sdtmndtasgtdt0(xv,xR,X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,plain,
! [X84,X85,X86,X87,X92] :
( ( aElement0(esk6_4(X84,X85,X86,X87))
| ~ aElement0(X85)
| ~ aElement0(X86)
| ~ aElement0(X87)
| ~ aReductOfIn0(X86,X85,X84)
| ~ aReductOfIn0(X87,X85,X84)
| ~ isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( sdtmndtasgtdt0(X86,X84,esk6_4(X84,X85,X86,X87))
| ~ aElement0(X85)
| ~ aElement0(X86)
| ~ aElement0(X87)
| ~ aReductOfIn0(X86,X85,X84)
| ~ aReductOfIn0(X87,X85,X84)
| ~ isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( sdtmndtasgtdt0(X87,X84,esk6_4(X84,X85,X86,X87))
| ~ aElement0(X85)
| ~ aElement0(X86)
| ~ aElement0(X87)
| ~ aReductOfIn0(X86,X85,X84)
| ~ aReductOfIn0(X87,X85,X84)
| ~ isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aElement0(esk7_1(X84))
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aElement0(esk8_1(X84))
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aElement0(esk9_1(X84))
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aReductOfIn0(esk8_1(X84),esk7_1(X84),X84)
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aReductOfIn0(esk9_1(X84),esk7_1(X84),X84)
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( ~ aElement0(X92)
| ~ sdtmndtasgtdt0(esk8_1(X84),X84,X92)
| ~ sdtmndtasgtdt0(esk9_1(X84),X84,X92)
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mWCRDef])])])])]) ).
fof(c_0_10,plain,
! [X56,X57,X58] :
( ~ aElement0(X56)
| ~ aRewritingSystem0(X57)
| ~ aReductOfIn0(X58,X56,X57)
| aElement0(X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mReduct])])]) ).
fof(c_0_11,negated_conjecture,
! [X111] :
( ~ aElement0(X111)
| ~ sdtmndtasgtdt0(xu,xR,X111)
| ~ sdtmndtasgtdt0(xv,xR,X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
cnf(c_0_12,plain,
( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X4,X1))
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aElement0(X1)
| ~ aReductOfIn0(X4,X3,X2)
| ~ aReductOfIn0(X1,X3,X2)
| ~ isLocallyConfluent0(X2)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( aElement0(X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aReductOfIn0(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( ~ aElement0(X1)
| ~ sdtmndtasgtdt0(xu,xR,X1)
| ~ sdtmndtasgtdt0(xv,xR,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X4,X1))
| ~ isLocallyConfluent0(X2)
| ~ aReductOfIn0(X4,X3,X2)
| ~ aReductOfIn0(X1,X3,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_16,hypothesis,
isLocallyConfluent0(xR),
inference(split_conjunct,[status(thm)],[m__656_01]) ).
cnf(c_0_17,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__656]) ).
cnf(c_0_18,plain,
( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X1,X4))
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X4)
| ~ aReductOfIn0(X1,X3,X2)
| ~ aReductOfIn0(X4,X3,X2)
| ~ isLocallyConfluent0(X2)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( ~ sdtmndtasgtdt0(xu,xR,esk6_4(xR,X1,X2,xv))
| ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(esk6_4(xR,X1,X2,xv))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_20,plain,
( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X1,X4))
| ~ isLocallyConfluent0(X2)
| ~ aReductOfIn0(X4,X3,X2)
| ~ aReductOfIn0(X1,X3,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_18,c_0_13]),c_0_13]) ).
cnf(c_0_21,plain,
( aElement0(esk6_4(X1,X2,X3,X4))
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aReductOfIn0(X4,X2,X1)
| ~ isLocallyConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(esk6_4(xR,X1,xu,xv))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]),c_0_17])]) ).
cnf(c_0_23,plain,
( aElement0(esk6_4(X1,X2,X3,X4))
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X4,X2,X1)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_21,c_0_13]),c_0_13]) ).
cnf(c_0_24,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16]),c_0_17])]) ).
cnf(c_0_25,hypothesis,
aReductOfIn0(xv,xa,xR),
inference(split_conjunct,[status(thm)],[m__779]) ).
cnf(c_0_26,hypothesis,
aReductOfIn0(xu,xa,xR),
inference(split_conjunct,[status(thm)],[m__755]) ).
cnf(c_0_27,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__731]) ).
cnf(c_0_28,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COM017+1 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 4 16:20:02 EDT 2026
% 0.15/0.35 % CPUTime :
% 0.19/0.36 % start to proof: theBenchmark
% 1.31/1.74 % Version : CSE_E---1.7
% 1.31/1.74 % Problem : theBenchmark.p
% 1.31/1.74 % SZS status Theorem for theBenchmark.p
% 1.31/1.74 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.369s
%------------------------------------------------------------------------------